A multisite analysis of temporal random errors in soil CO2 ...udel.edu/~rvargas/Vargas/Publications_files/Cueva_etal_2015_JGR... · A multisite analysis of temporal random errors

A multisite analysis of temporal random errorsin soil CO2 effluxAlejandro Cueva1,2, Michael Bahn3, Marcy Litvak4, Jukka Pumpanen5, and Rodrigo Vargas6

1Departamento de Biologa de la Conservacin, Centro de Investigacin Cientfica y de Educacin Superior de Ensenada,Ensenada, Mexico, 2Programa de Posgrado en Ciencias de la Tierra. Divisin de Ciencias de la Tierra, Centro de InvestigacinCientfica y de Educacin Superior de Ensenada, Ensenada, Mexico, 3Institute of Ecology, University of Innsbruck, Innsbruck,Austria, 4Department of Biology, University of New Mexico, Albuquerque, New Mexico, USA, 5Department of ForestSciences, University of Helsinki, Helsinki, Finland, 6Department of Plant and Soil Sciences, University of Delaware,Newark, Delaware, USA

Abstract An important component of the terrestrial carbon balance is the efflux of CO2 from soils tothe atmosphere, which is strongly influenced by changes in soil moisture and temperature. Continuousmeasurements of soil CO2 efflux are available around the world, and there is a need to develop and improveanalyses to better quantify the precision of themeasurements. We focused on random errors in measurements,which are caused by unknown and unpredictable changes such as fluctuating environmental conditions.We used the CO2 gradient flux method with two different algorithms to study the temporal variation of soilCO2 efflux and associated random errors at four different ecosystems with wide ranges in mean annualtemperature, soil moisture, and soil CO2 efflux. Our results show that random errors were better explainedby a double-exponential distribution, had a mean value close to zero, were nonheteroscedastic, and wereindependent of soil moisture conditions. Random errors increased with the magnitude of soil CO2 efflux andscale isometrically (scaling exponent 1) within and across all sites, with a single relation common to all data.This isometric scaling is unaffected by ecosystem type, soil moisture conditions, and soil CO2 efflux range(maximum and minimum values within an ecosystem). These results suggest larger uncertainty underextreme events that increase soil CO2 efflux rates. The accumulated annual uncertainty due to random errorsvaried between 0.38 and 2.39%. These results provide insights on the scalability of the sensitivity of soilCO2 efflux to changing weather conditions across ecosystems.

1. Introduction

An important component of terrestrial CO2 fluxes are the fluxes of CO2 from soils to the atmosphere. The totalsoil CO2 efflux is a combination of two principal components: (a) respiration derived from carbon assimilatedby plants (by roots and mycorrhiza; autotrophic respiration) and (b) a component derived from carbonrespired during the decomposition of dead plant litter and microbial debris (heterotrophic respiration)[Bahn et al., 2010a; Hanson et al., 2000; Kuzyakov, 2006; Ryan and Law, 2005]. Furthermore, soil CO2 effluxhas complex dynamics that vary on different temporal and spatial scales [Vargas et al., 2011a] as a resultof changes in biotic (e.g., quantity and quality of organic matter and photosynthetic activity) and abiotic(e.g., temperature, soil texture, moisture, bulk density of soil, and diffusion of gases in soil) factors[Kuzyakov, 2002; Pumpanen et al., 2003].

Technological advances in the last decade have increased the number of automated measurements of CO2fluxes at the ecosystem level [Baldocchi, 2008] and for soil CO2 efflux [Vargas et al., 2011a]. In addition,the establishment of monitoring networks (e.g., FLUXNET, National Ecological Observatory Network(NEON), and Integrated Carbon Observation System (ICOS)) has increased the use of automatedmonitoring systems, resulting in growing data sets of continuous measurements of CO2 fluxes. With thiswealth of information it is now possible and necessary to characterize uncertainties in measurements tobetter constrain annual estimates and modeling approaches [Hollinger and Richardson, 2005; Richardsonet al., 2006; Savage et al., 2008]. While much attention has been placed on quantifying the uncertainties ofecosystem-scale CO2 fluxes, using the eddy covariance technique [Dragoni et al., 2007], the uncertaintiesassociated with soil CO2 measurements are relatively unknown [Savage et al., 2008]. Soil CO2 effluxrepresents the second largest flux for exchange of CO2 between the ecosystems and the atmosphere, and

CUEVA ET AL. RANDOM ERRORS IN SOIL CO2 EFFLUX 1

PUBLICATIONSJournal of Geophysical Research: Biogeosciences

RESEARCH ARTICLE10.1002/2014JG002690

Key Points: Random errors of CO2 efflux wereexplored at four ecosystems

Random errors were independent ofsoil moisture conditions

Random errors scale isometrically withsoil CO2 efflux rates

Supporting Information: Supporting Information S1 Supporting Information S2 Figure S1

Correspondence to:R. Vargas,[email protected]

Citation:Cueva, A., M. Bahn, M. Litvak, J. Pumpanen,and R. Vargas (2015), A multisite analysisof temporal random errors in soil CO2efflux, J. Geophys. Res. Biogeosci., 120,doi:10.1002/2014JG002690.

Received 22 APR 2014Accepted 20 MAR 2015Accepted article online 26 MAR 2015

2015. American Geophysical Union. AllRights Reserved.

http://publications.agu.org/journals/http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2169-8961http://dx.doi.org/10.1002/2014JG002690http://dx.doi.org/10.1002/2014JG002690

this flux exceeds by an order of magnitude, the contribution of CO2 due to the combustion of fossil fuels[Bond-Lamberty and Thomson, 2010]. Therefore, it is critical to accurately estimate uncertainties to betterquantify local-to-global carbon balance.

Soil CO2 efflux (Fsoil) could be reported as hourly, daily, monthly, or annual rates, but there is no consensus onhow to report errors and uncertainties in these and other biometeorological measurements. The definitionsof what are considered as measurement errors and uncertainty is arguable. For example, Regan et al. [2002]defines the term error as a result of imperfections in measuring equipment and observationaltechniques and includes operator error and instrument error, while (epistemic) uncertainty is associatedwith knowledge of the state of a system and it includes limitations of measurement devices, insufficientdata, extrapolations or interpolations, and variability over time or space. On the other hand, Billesbach[2011] defines the difference as: the term error connotes a situation that can or should be corrected,minimized, or otherwise accounted for, while the term uncertainty suggests a quantification of theprecision of a measurement. Meanwhile, Richardson et al. [2012] defines error as a single value indicatingthe difference between an individual measurement and the actual or true quantity being measured,whereas uncertainty is a range of values characterizing the limits within which the quantity beingmeasured could be expected to fall.

In this study, we define uncertainty as a range of values where an individual measurement is expected to fall.We clarify that uncertainty includes limitations attributable to systematic and random errors that influencethe precision of a measurement. Therefore, uncertainty is a range of values that characterize the limitswithin which soil CO2 efflux measurements are expected to fall.

The measured CO2 efflux (FsoilM) is a composite of Fsoil and systematic () and random () errors, such thatFsoilM = Fsoil + + , as described for ecosystem-scale fluxes [Richardson et al., 2006]. Systematic errors () inexperimental observations usually come from the measuring instruments due to improper calibration ormistakes in data handling by the system [Campbell et al., 2013]. Fortunately, improvements in technologyand constant equipment calibration can minimize . Random errors () in experimental measurements arecaused by unknown and unpredictable changes in the experiment such as changes in environmentalconditions that affect the performance of the measurements. It is important to recognize that randomerrors do not affect the average of the measurements, but they change the distribution of themeasurements and therefore the variability around this average.

In this study, we focus on how random errors in soil CO2 efflux respond to changes in soil moisture acrossmultiple vegetation types. This analysis is important because (a) soil CO2 efflux is influenced by changes insoil CO2 diffusion rate, which is dependent on changes in soil water content [imnek and Suarez, 1993];and (b) metabolic activity, leading to the production of CO2 in soil, is strongly influenced by soil moisture[Moyano et al., 2012]. It is expected that global environmental change will influence patterns of precipitationand water availability around the world [Foley et al., 2003; Loik et al., 2004]. Consequently, changes inprecipitation are likely to alter ecosystem CO2 dynamics across terrestrial ecosystems [Knapp et al., 2008;Reichstein et al., 2013; Vargas et al., 2012; Vicca et al., 2014], due to feedbacks and interactions betweenbiogeochemical cycles [Heimann and Reichstein, 2008]. Thus, it is critical to understand how changes in soilmoisture and water availability will influence soil CO2 effluxes and associated to measurements.

The soil CO2 gradient method is a widely used approach to measure soil CO2 efflux (F) across manyecosystems and is based on measurements of soil profiles of CO2 concentrations and a diffusion model[Hirano et al., 2003; Jassal et al., 2005; Maier and Schack-Kirchner, 2014; Tang et al., 2003; Vargas et al., 2010].Unfortunately, it is still unknown how changes in soil moisture influence random errors in F both withinand across different ecosystems. To address this knowledge gap, we establish three main objectives:First, to identify differences (if any) in estimations of F using two frequently used algorithms for the CO2gradient method [Pumpanen et al., 2008; Vargas et al., 2010] across multiple ecosystems. Second, todetermine patterns of random errors across different ranges of soil moisture (i.e., low, medium, and high)across ecosystems. This is particularly important because there is evidence that, for example, empiricalmodels tend to underestimate F at low soil moisture conditions [Reichstein et al., 2003], meanwhile otherstudies [Kim et al., 2012; Xu et al., 2004] had highlighted the importance of the impact of high soil moistureconditions on F [Vargas et al., 2011b]. Third, to determine relationships (if any) between random errors andsoil moisture and the magnitude of F across ecosystems.

Journal of Geophysical Research: Biogeosciences 10.1002/2014JG002690


We postulate four hypotheses: (H1) different F gradient algorithms yield similar efflux rates (i.e., notstatistically different); (H2) total random errors may be similar between F gradient algorithms (i.e., notstatistically different and with similar statistical characteristics). H1 and H2 are expected because differentgradient algorithms have a similar representation of the physical process, as well as similar inputparameters (e.g., CO2 concentrations, soil moisture, and soil physical properties). The results from bothalgorithms are based on the Ficks law of diffusion, which is influenced by changes in soil moisture andtherefore the air-filled porosity within the soil. Therefore, we postulate that (H3) differences betweenrandom errors and F are likely to be larger at both high (wetter) and low (dryer) soil moisture due tochanges in soil CO2 diffusivity and metabolic processes that drive soil CO2 efflux. This is expected becausethe magnitude of soil CO2 efflux from the algorithms may be more sensitive at either higher or lower soilmoisture, where the influence of soil CO2 diffusivity differs from that of the metabolic processesunderpinning soil CO2 efflux [Pingintha et al., 2010]. (H4) The statistical characteristics and distribution ofrandom errors for soil CO2 efflux across ecosystems will be similar to those random errors present in othermeasurements of ecosystem CO2 fluxes. H4 is expected because there is evidence that using differentsensors (e.g., closed-path/open-path infrared gas analyzers [Richardson et al., 2006]) and methods (e.g., soilrespiration chambers [Savage et al., 2008]) to measure ecosystem CO2 fluxes, as well as approaches toestimate random errors (e.g., model residuals, paired instruments, and paired observations; see section 2.3for description), converge in similar statistical characteristics of random errors.

2. Methods2.1. Study Sites

The current study uses continuous time series (30min resolution) of soil CO2 efflux, temperature, andmoisture from four different ecosystems: temperate mixed forest, boreal forest, temperate grassland, andarid woodland (Table 1).

The James San Jacinto Mountains Reserve (Jre) is part of the University of California Natural Reserve Systemand is located in Southern California, Unites States. The Jre is a mixed conifer and oak temperate forest with amean annual precipitation (MAP) of 507mm and amean annual temperature (MAT) of 10.3C. The soil in Jre isclassified as Entisol, and detailed site characteristics are described in Table 1. The Jre is instrumented withsolid-state CO2 sensors (CARBOCAP, GMM 220, Vaisala, Helsinki, Finland), which are nondispersive infraredsensors for the measurement of gaseous CO2 within the soil, and additional sensors for soil temperatureand moisture (ECHO, Decagon, Pullman, WA) within the soil at 2, 8, and 16 cm depth [Vargas and Allen, 2008].

The second site is located in Hyytil (Hyy) in the Station for Measuring Forest-Ecosystem-AtmosphereRelations II measuring station in southern Finland. The vegetation is characterized by a 52 year old borealconiferous forest with a MAP of 700mm and a MAT of 2.9C. The soil in Hyy is classified as Haplic podzol,and detail site characteristics are described in Table 1. The Hyy site is instrumented with solid-state CO2sensors (CARBOCAP, GMM 220, Vaisala, Helsinki, Finland) to measure CO2 concentrations, and additionalsensors for soil temperature (Philips KTY thermistors, Eindhoven, Netherlands) and moisture (TDR-100,Campbell Scientific, Inc.) within the soil at 0, 2, 12, and 20 cm depth [Pumpanen et al., 2008].

The third site is located at the Stubai Valley (Stu), located in the vicinity of Neustift, Austria. The Stu site is atemperate mountain grassland, with a MAP of 850mm and a MAT of 6.3C. The soil in Stu is classified asFluvisol, and detail site characteristics are described in Table 1. The Stu site is instrumented with solid-stateCO2 sensors (CARBOCAP, GMT222, Vaisala, Helsinki, Finland) to measure CO2 concentrations at 5 and 10 cm

Table 1. Sites and Years Used and Main Characteristicsa

Site Latitude Longitude DY Soil TypeSand(%)

Silt(%)

Clay(%)

BD(mg/m3)

P(m3/m3) Vegetation Type

MAT(C)

MAP(mm)

Jre 3348N 11646W 2006 Entisol 83 10 7 1.2 0.55 Temperate forest 10.3 507Hyy 6151N 24117W 2010 Podzol haplic 69 20 11 0.6 0.61 Boreal forest 2.9 700Stu 4707N 1119W 2006 Fluvisol 42 31 27 0.91 0.66 Temperate grassland 6.3 850Nme 3426N 10614W 2012 Turkey Springs stony loam 35 40 25 1.16 0.56 Semiarid woodland 14.8 418

aDY: data year; BD: bulk density; P: porosity; MAT: mean annual temperature; MAP: mean annual precipitation.



depth. Microclimate data were recorded continuously and logged at half-hourly intervals with an automatedstation, and included soil temperature (averaging soil thermocouple probe TCAV; Campbell Scientific) andmoisture (ML2x; Delta-T Devices, Cambridge, UK) at 5 and 10 cm soil depth [Wohlfahrt et al., 2008].

The fourth site is located within the New Mexico Elevation Gradient, in the United States (Nme) [Anderson-Teixeira et al., 2011]. The Nme site is a pion-juniper woodland, with a MAP of 418mm and a MAT of 14.8C.The soil in Nme is classified as Turkey Springs stony loam and detail site characteristics are described inTable 1. The Nme is instrumented with solid-state CO2 sensors (CARBOCAP, GMT221, and GMT222,Vaisala, Helsinki, Finland) to measure CO2 concentrations, colocated with sensors for soil temperatureand moisture (TDR-100 and T107 probes, Campbell Scientific, Inc.) within the soil at 5, 10, 20, and 40 cmdepth [Anderson-Teixeira et al., 2011].

2.2. Calculation of F Using the Gradient Method

We used two algorithms to calculate F through the gradient method described by Vargas et al. [2010](thereafter A1) and Pumpanen et al. [2008] (thereafter A2). Calculations of CO2 efflux for A1 and A2 arebased on the Ficks law of diffusion:

F Ds CZ

(1)

where F is the soil CO2 efflux (molm2 s1); DS is the coefficient of diffusion (m

2 s1); C is the CO2 moledensity (molm3) computed using the universal gas law; and Z is the depth (m). To calculate the soilCO2 efflux, A1 uses the diffusion model proposed by Moldrup et al. [1999] (equation (2)), and A2 is basedon Troeh et al. [1982] CO2 diffusion model (equation (3)):

DsDa1

2

S(2)

DsDa2

u1 u

h(3)

where Da1 is the effect of temperature and pressure; Da2 is the effect of temperature; is a constant ( = 2.9);S= silt + sand; u and h are dimensionless constants that describe the tortuosity of the soil obtained in theliterature [Glinski and Stepniewski, 1985]; is the air-filled porosity (equation (4)); and is the porosity(equation (5)):

(4)

1 Bulk densityParticle density

(5)

where is the soil water content (m3m3), and the particle density is a constant (2.65 g cm3). The effect ofthe temperature (Da2) and pressure (Da1) are given by the following:

Da1 Da0 TT0

1:75 P0P

(6)

Da2 1:997 log T 9:7273 (7)

where Da0 is a reference value (1.47 1015m2 s1) at T0 (293.15 K) and P0 (1.013 10

5 Pa); T is thetemperature (K), and P is the pressure (Pa).

Both algorithms (A1 and A2) incorporate the gaseous diffusion coefficient of CO2 at specific depths within thesoil profile (e.g., 28 cm and 816 cm) to calculate F. To calculate F in the soil surface (Z= 0) A1 uses a linearextrapolation assuming CO2 production is constant across the soil profile. Meanwhile A2 uses the differenceof CO2 concentrations between the atmosphere and the shallowest measurement in the soil layer. For A2 weused a constant value for atmospheric CO2 of 380 ppm for Jre and Nme, and for Hyy we used measurementsof ambient CO2 concentrations made by an automated CO2 efflux chamber located at 15 cm above the soilsurface. For A1 and A2 at Stu we used measurements made by an eddy covariance tower at 2m height foratmospheric CO2 concentrations [Vargas et al., 2011b]. Furthermore, for Hyy and Stu we restricted ouranalysis to data from snow-free periods.



2.3. Data Analysis

There are different methods to calculate random errors in flux measurements, mainly explained in the eddycovariance literature. The model residuals approach [Lasslop et al., 2008;Menzer et al., 2013; Richardson et al.,2012] infers the errors from the difference between model predictions and measurements from instruments[Richardson et al., 2008; Vargas et al., 2013]. The paired instruments [Schmidt et al., 2012] or two towers[Hollinger et al., 2004] approach uses the difference of two similar instruments/towers that measure at thesame time and place to estimate the random errors [see Kessomkiat et al., 2013]. Since the pairedinstruments approach could be difficult to implement, the paired observation approach trades space fortime [Hollinger and Richardson, 2005; Richardson et al., 2006; Savage et al., 2008], to estimate the randomerrors from the difference of two measurements made at the same location but with a time difference(e.g., 24 h). This paired observation approach is ideal to calculate random errors for F because soil isspatially heterogeneous (from the microscale to the ecosystem level), and the physical conditions changeacross spatial scales influencing the biophysical controls on F [Leon et al., 2014].

Here the paired observation approach was used to infer the statistical properties of the random errors () in Ffor each site:

Ft0 Ft24ffiffiffi2

p (8)

where Ft = 0 is the soil CO2 efflux calculated at time zero and Ft = 24 is the soil CO2 efflux calculated exactly 24 hlater. To ensure that differences in these paired measurements were attributed to random errors and not toexternal abiotic effects (e.g., rapid changes due to precipitation events), we established two conditions:for each pair of days (i.e., measurements taken at 24 h of difference) the second day (i.e., Ft=24, , Ft=47of the day dt + 1) must have similar conditions of soil moisture () and soil temperature (Ts) as thefirst day (Ft = 0, , Ft = 23 of the day dt). To establish the similarity between days, we used the range ofX,dt + 2X,dt>X,dt + 1>X,dt 2X,dt, where is the statistical average and is the standard deviationand X refers to or Ts, in that way the mean value of and Ts for the second day (dt + 1) have to bebetween X 2X of and Ts for the first day (dt). If these conditions were not met, then themeasurements were not considered for the calculation of random errors as we assumed that there weredifferent environmental conditions between pairs of days [Cueva et al., 2012].

To test H1 (similar efflux rates between algorithms) and H3 (differences between and F at high and low ),we determined intermediate, low, and high conditions of by establishing three different site-dependentthresholds. Intermediate conditions were defined as ( +0.5> N>0.5), low conditions weredefined as (L + 0.5) for each site. Thus, theconditions of are dependent on the soil moisture patterns at each site and reflect the site-specificweather and soil conditions.

To test H4, we tested previous observations that the distribution of random errors is better explainedby a double-exponential distribution or Laplace distribution, in comparison with a normal or Gaussiandistribution [Hagen et al., 2006; Hollinger and Richardson, 2005; Richardson and Hollinger, 2005; Richardsonet al., 2006, 2008; Savage et al., 2008], by fitting a double-exponential distribution defined by the following:

f x e x=j =2 (9)

The double-exponential distribution has a standard deviation defined by = (2), with as an unbiasedestimator defined by the following:

XN

i1 xi xj jN

(10)

The double-exponential distribution is characterized by a pronounced central peak and longer tails than aGaussian distribution. Furthermore, the Gaussian distribution comprises 68% of the data in 1, whereasthe double-exponential distribution encompasses 76%.

To analyze relationships of random errors under different environmental conditions, data were binnedaccordingly to different conditions of , soil CO2 efflux, or time lapses (e.g., day and month). Bins



of random errors were made usingthe standard deviation from thedouble-exponential distribution (())as an estimate of uncertaintythe precision of the measurementat a specific moment in certainenvironmental conditions [Hollingerand Richardson, 2005]. In this waywe were able to explore how theuncertainty, which is influenced byrandom errors, scales according tothe different environmental conditions.Furthermore, we explored how allavailable data on () scales with soil

CO2 efflux within and across sites. There is evidence that fundamental characteristics of plants andecosystems scale with kinetic of metabolic reactions [Enquist et al., 2003, Reich et al., 2003]. Thus, we usea general form described by a power law:

Y Y0Fb (11)

where Y is an attribute such as (), Y0 is a normalization constant, F is soil CO2 efflux, and b is the scalingexponent. Type II linear regression was used to fit slopes between log () and log F within and amongsites. The slope of such regressions is equivalent to the scaling exponent of a power law (equation (11)).

Differences between means were evaluated using 95% confidence intervals (CIs), calculated using abootstrap analysis with 1000 runs. Thus, if the 95% CIs of mean did not overlap, then differences wereconsidered to be significant at P< 0.05. The nonparametric Kolmogorov-Smirnov test was used to evaluateif the distribution of the random errors followed a Gaussian distribution. To estimate the accumulated

Table 2. Annual Means of Soil CO2 Efflux and Soil Water Content by Siteand Algorithma

Site A F (mol CO2m2 s1) (m3m3)

Jre A1 0.89 0.49 0.12 0.05A2 0.87 0.58

Hyy A1 1.33 0.57 0.28 0.07A2 2.11 1.37

Stu A1 2.21 2.34 0.35 0.10A2 2.82 2.97

Nme A1 0.05 0.04 0.09 0.03A2 0.10 0.03

aSee section 2 for description of algorithms used to calculate soil CO2efflux. A: Algorithm to calculate soil CO2 efflux; F: soil CO2 efflux (mean standard deviation); : soil water content (mean standard deviation).

Figure 1. (ad) Daily average for soil CO2 efflux for A1 (black line) and A2 (grey line) and (eh) daily average for soil watercontent divided by ranges (light grey is L, dark grey is H, and white is N) for the four sites. See section 2 for sitedescriptions: Jre: temperate forest; Hyy: boreal forest; Stu: temperate grassland; Nme: semiarid woodland.



uncertainty over the seasons on soil CO2 efflux estimated by A1 and A2, a bootstrap analysis with 1000 runswere used to estimate the 95% CI of the daily standard deviation of random errors. All the analyses weremade using MATLAB (R2010b; Mathworks Inc., Natick, MA, USA).

3. Results3.1. Assessment of Soil CO2 Efflux Rates

Daily averages of F were calculated using A1 and A2 (Table 2). Both algorithms had similar generaltemporal patterns for F at all sites, and there were no significant differences (P> 0.05) in means at Jre,Hyy, and Stu, but there were differences at Nme; furthermore, there were substantial mismatches forextreme high fluxes at each site (Figures 1a1d). The daily average of soil moisture () showedcontrasting differences in climate among sites represented in the temporal variation of high andlow soil moisture conditions (Figures 1e1h).

3.2. Distribution of Random Errors

The distribution of the random errors using the paired observation approach was characterized by long tailsand a central peak (Figure 2). A Kolmogorov-Smirnov test indicated that the distributions were not Gaussian(P< 0.001; Table 3) for any site or algorithm (i.e., A1 and A2). The strong kurtosis presented in almost alldistributions (>10, except for Nme; Table 3) suggests a double-exponential (Laplace) distribution forrandom errors (Figure 2). In some cases, the distribution was symmetric because the skewness was closeto zero, but in others there was a negative or positive skew (Table 3), making the distribution asymmetric(Figure 2). The mean value of the total random errors was close to zero (Table 3) for all the study sites, andthere were no significant differences (P> 0.05) between random errors across algorithms. The standarddeviation of the random errors tended to be consistently higher for A2 across all sites.

Figure 2. Histograms of frequencies of random errors for different algorithms ((ad) A1 and (eh) A2) to calculate soil CO2efflux for the four sites. The solid black line represents a Gaussian distribution, whereas the solid grey line represents adouble-exponential distribution. See section 2 for site descriptions: Jre: temperate forest; Hyy: boreal forest; Stu: temperategrassland; Nme: semiarid woodland.



When random errors were sorted by different soil moisture () conditions, themean value tended to be close tozero for all algorithms and sites (Table 4). There were no significant differences in random errors betweenalgorithms (i.e., A1 and A2) across the selected ranges of (Table 4). We found different patterns for thecharacteristics of the distribution of random errors between algorithms; especially for the Jre and Hyy sites.For example, in Jre and Stu for the L range the skewness was higher than for N and H; meanwhile for Hyythe skewness was higher for A2 than A1. In contrast, for Nme the skewness was consistently close to zero.

3.3. Scaling Relationships of Random Errors

When random errors (from both algorithms) were binned across different environmental conditions, wefound that the standard deviation of random errors (()), a quantification of uncertainty, scaled accordingto the flux magnitude but not with changes in (supporting information Figure S1). Using hourly data,

Table 3. Statistical Properties of Total Random Errors ()a

Site A N()

(mol CO2m2 s1)

CI () (95%)(mol CO2m

2 s1)()

(mol CO2m2 s1)

(2)(mol CO2m

2 s1) S K KS

Jre A1 4,680 0.0004 0.0034, 0.0043 0.14 0.13 0.21 12.96

we found that () scaled approximatelyisometrically (scaling exponent 1)with F (Figure 3). This pattern wassignificant (P< 0.05) within vegetationtypes and when all data are analyzedjointly in one general regression(Figure 3e). Furthermore, we found aseasonal pattern of () (Figure 4) thatmimics the pattern of F across theyear (Figure 1), supporting that theuncertainty increased according to fluxmagnitude. No significant relationships(P> 0.05) were found when we binned() accordingly to ; thus, uncertaintydid not scale with changes in soilmoisture.

3.4. Random Errors and ItsContribution to SeasonalSoil CO2 Efflux

We estimated the accumulateduncertainty influenced by randomerrors across all measured days forthe different F algorithms using abootstrap analysis. Since we had todiscard data that did not meet theconditions of similar days required toestimate random errors, we estimated95% CI related to the variation ofrandom errors as a representation ofthe accumulated uncertainty. Thestudy site with the largest seasonalsum for F was Stu (grassland) andthe lowest was Nme (arid woodland),while Jre (temperate mix forest) andHyy (boreal forest) had relativelysimilar annual sums (Table 5). Theseseasonal sums for F are dependenton the number of available dayswith measurements therefore donot represent a total annual flux.The accumulated uncertainty variedbetween 0.11 (0.38% of the seasonalsum) (at Nme) and 18.5 (2.39% of

the seasonal sum) (at Stu) g Cm2 season1 (Table 5) across sites at 95% confidence. In general, A2 hadlarger accumulated uncertainty values in comparison to A1, but no statistical differences were found.

4. Discussion

Our results support H1, in that we did not find significant differences in daily means and temporal patternsof soil CO2 efflux (F) between algorithms (i.e., A1 and A2). Random errors were not significantly differentbetween algorithms and across sites and, in general, had similar statistical characteristics, partiallysupporting H2. Furthermore, random errors were not significantly different among different soil watercontent () conditions and algorithms (not supporting H3), but we found that the uncertainty related to

Figure 3. Relationship between log-transformed (standard deviation ofrandom errors) and log-transformed soil CO2 efflux (F) (ad) within sitesand (e) across all sites. Results for Figure 3e include m = 1.12 0.01;r2 = 0.72; RMS error = 1.146; n = 28800. The slope of such regressions(m) is equivalent to the scaling exponent of a power law. All slopes ofregression lines are significant (P< 0.05). See section 2 for site descriptions:Jre: temperate forest (Figure 3a); Hyy: boreal forest (Figure 3b); Stu:temperate grassland (Figure 3c); Nme: semiarid woodland (Figure 3d).



random errors scaled isometrically(scaling exponent 1) with F withinand across all sites. Finally, we foundthat the statistical properties anddistribution of random errors using thegradient method and both algorithms(i.e., A1 and A2) were similar tothose presented in ecosystem-scalemeasurements and soil respirationchambers (supporting H4). Here wediscuss the implications of these results.

The algorithms used to calculate F(i.e., A1 and A2) gave similar temporalpatterns of F. Daily means were notsignificantly different in Hyy, Jre, andStu (supporting H1), but we founddifferences in Nme. The mismatchesbetween A1 and A2 were consistentwhen larger fluxes were present(Figure 1) and therefore bring attentionto potential systematic errors whenhigh CO2 efflux rates occurred. Thedifferences found in Nme indicate thatthe algorithms could be sensitive tosite-specific characteristics, or a Type Istatistical error due to the very smallmagnitude of F and limited data. Wepropose that further testing againstother techniques (e.g., soil respirationchambers) and a longer record ofmeasurements are needed to identifytrends and differences at this studysite. We argue that in most casesthere should be good agreementbetween algorithms because they havea similar representation of the physicalprocesses and have similar inputparameters (e.g., CO2 concentrations,soil moisture, soil temperature, andsoil physical properties).

Our data set of continuousmeasurements allowed us to quantifythe temporal variability of randomerrors. We demonstrated that randomerrors followed similar temporalpatterns despite the algorithm used forcalculating F and the ecosystem type(partially supporting H2). The statisticalcharacteristics and distribution ofrandom errors was similar to those

found for ecosystem-scale measurements [cf. Richardson et al., 2006], supporting H4. The mean valueof total random errors across sites, regardless of the algorithm to calculate F, was constantly near zero.Their distribution was not Gaussian and was better approximated by a double-exponential distribution

Figure 4. Seasonal variation of the standard deviation of random errorsin soil CO2 efflux across sites. Colors represent different algorithms tomeasure soil CO2 efflux: A1 = black circles; A2 = grey circles. See section 2section for description of algorithms to calculate soil CO2 efflux. See section 2for site descriptions: (a) Jre: temperate forest; (b) Hyy: boreal forest; (c) Stu:temperate grassland; (d) Nme: semiarid woodland.



(i.e., long tails and prominent centralpeak; Table 3 and Figure 2), as hasbeen found for random errorsin eddy covariance measurements[Richardson et al., 2006].

The convergence that randomerrors have a similar distribution(i.e., double-exponential distribution)across different ecosystem CO2 fluxesmeasured using different methods(e.g., eddy covariance, soil respirationchamber, and gradient method) couldbe explained by the approach usedto calculate these random errors.Random errors using the pairedobservation approach [Richardsonet al., 2006] are estimated by thedifference of two measurements with

a temporal lag between them, divided by the square root of the number of observations (see equation (8)).Then, while the probability density function of a Gaussian distribution is expressed by the square difference(e.g., (X1 X2)2), the probability density function of a double-exponential distribution is expressed by theabsolute difference (e.g., |X1X2|), resulting in a distribution with larger tails and a more prominent centralpeak. We argue that if the paired observation approach is used to calculate random errors, then it will resultin a double-exponential distribution regardless of the measured ecosystem flux (e.g., CO2, N2O, and CH4) orthe ecosystem type (e.g., terrestrial, urban, and marine). We recognize that this statement should be testedin future studies.

Despite of the similarities in the distributions or randomerrors across sites and algorithms, we found differencesin the distribution properties of random errors between algorithms (i.e., A1 and A2; not supporting H2). Thestandard deviation for random errors was constantly higher at all sites for A2 than A1, showing a highervariation in random errors using A2. Furthermore, the skewness values for A1 were generally lower thanthose for A2, and higher values of kurtosis were constant in A2 than A1. Those differences may imply theexistence of a systematic error for A2, but detailed exploration for this explanation is outside the scopeof this work. The double-exponential distribution of random errors for both algorithms and across sitesdemonstrates that (a) larger random errors occur more frequently than expected from a Gaussiandistribution and (b) small random errors are more frequent than larger errors, and these small random errorsare also more common than expected from a Gaussian distribution (Figure 2). We suggest that the largevalues of random errors could be explained due to the approach used to calculate these values. The pairedobservation approach calculates random errors using two measurements in similar environmental conditionsseparated by 24h. Under this assumption, our approach does not take into account temporal lags that caninfluence the magnitude of the flux. Therefore, subsequent analyses of random errors for soil andecosystem-scale CO2 efflux should not only explore differences among weather conditions and studysites but also include potential lag effects that are important in the response of soil CO2 efflux rates[Bahn et al., 2009; Baldocchi et al., 2006; Vargas et al., 2011b].

Our results show that random errors were not significantly different among different conditions and thusdo not support H3. When random errors were sorted by different conditions (i.e., L, N, and H) themean value of random errors continued to be close to zero (Table 4), the distribution was better explainedby a double-exponential distribution, and we found consistently higher standard deviations for A2 than forA1. These results are consistent with the analysis of total random errors, as we also found differences inthe distribution properties of random errors when divided by conditions. We postulate that differencesin the properties of the distribution of random errors, when sorted by different conditions, couldindicate when random errors have a larger contribution to F estimations. For example, when the skewnessis not close to zero and there is a strong kurtosis (e.g., at Jre for A2 in L, at Stu for A1 in L), there couldbe a larger contribution of random errors under those conditions.

Table 5. Total Sums of CO2 Efflux (F) and Accumulated and RelativeUncertaintya

Site AFT

(g Cm2 season1)

AccumulatedUncertainty(g Cm2 y1)

RelativeAccumulatedUncertainty (%)

Jreb A1 335 184 3.02 0.89A2 325 216 4.83 1.48

Hyyb A1 252 108 3.56 1.40A2 402 261 5.88 1.46

Stub A1 605 641 13.72 2.26A2 773 800 18.50 2.39

Nmeb A1 14 11 0.17 0.81A2 27 8 0.11 0.38

aA: Algorithm to calculate soil CO2 efflux, A1 [Vargas et al., 2010] and A2[Pumpanen et al., 2008]; FT: total sum of daily means of F 1 standarddeviation; accumulated uncertainty based on random errors.

bFor Jre, Hyy, Stu, and Nme we calculated the total sum of soil CO2efflux for 365, 300, 262, and 188 days, respectively. Therefore, season1represents the number of days with available measurements.



Our results show that random errors in soil CO2 efflux rates were non-Gaussian, nonhomoscedastic, andnonindependent across different ecosystems. These results support previous observations using automatedchambers to measure soil CO2 efflux in a temperate forest [Savage et al., 2008]. Information about statisticalproperties of random errors could help in applying different approaches (e.g., Monte Carlo simulations andbootstrap reanalysis) to calculate specific parameters in empirical models [e.g., Richardson and Hollinger,2005], as well as on improving gap-filling methods for soil CO2 efflux [Gomez-Casanovas et al., 2012;Richardson and Hollinger, 2007].

In general, we found a significant relationship between the standard deviation of random errors (()) and F(supporting information Figure S1), but we did not find a significant relationship between and () atdifferent temporal scales (e.g., day, season, and year; rejecting H3) or soil water content conditions (i.e., L,N, or H; rejecting H3). Our results support previous findings that random errors scale with flux magnitude[Richardson et al., 2006; Savage et al., 2008], and these studies have suggested a correction factor of 1/

ffiffiffin

pto decrease random errors.

Another novel aspect of our study is the fact that () scales approximately isometrically (scaling exponent< 1)with F. These patterns were found to be highly significant within ecosystem types and when all data wereanalyzed jointly in one general regression. Therefore, these results support evidence that fundamentalcharacteristics of ecosystems could follow power relationships [Enquist et al., 2003, Reich et al., 2003]. Weacknowledge that there is substantial variability in the observations that is not explained by the linearmodels (i.e., relatively low r2 values), and the strength of the scaling of random errors across F should beexplored across a wider range of ecosystems and magnitudes of F. We believe that these results open newresearch questions about the scaling of () across other ecosystem fluxes; especially those measuredusing eddy covariance [Dragoni et al., 2007].

Our results suggest higher uncertainty (or imprecision of a measurement) in larger measured fluxes as apotential result of extreme events such as hurricanes [Vargas, 2012], or rewetting and thawing events [Kimet al., 2012; Leon et al., 2014]; therefore, further analyses are needed under these rare but importantevents. Furthermore, these results suggest that when gap-filling methods are applied to soil CO2 effluxmeasurements [Gomez-Casanovas et al., 2012], uncertainty on those estimations could be higher whenrelative high fluxes are expected, coupled with the inherent model error from the gap-filling method ofecosystem-scale fluxes [Richardson and Hollinger, 2007].

The accumulated uncertainty (()) varies among sites and algorithms between 0.11 and 18.5 gCm2 season1

(Table 5). In relative terms, the accumulated uncertainty varied between 0.38 and 2.39% of the seasonal CO2efflux across sites. These values of uncertainty could vary depending of the length of the data [Liu et al., 2009;Loescher et al., 2006], the frequency of the measurements, the magnitude of fluxes [Richardson et al., 2006], andthemethod to calculate random errors [Menzer et al., 2013; Richardson and Hollinger, 2005]. For example, the Stusite had not only the highest uncertainty due to random errors but also the highest magnitude of F (Figure 1),the highest total annual sum (Table 5), and the highest daily variability (Table 2) that is translated into a largestandard deviation in the annual sum (Table 5). These fluxes are expected as, the Stu site, like othermountain grasslands, is characterized by high annual sums compared to others ecosystems globally [Bahnet al., 2010b]. In this way, our estimates of accumulated () not only have to be taken as upper limits butalso suggest that they represent a small but quantifiable influence of random errors in the total seasonalsums of F. Systematic assessments with longer time series are needed to identify patterns of random errorsacross different ecosystems and climate conditions.

There are advantages and disadvantages across different approaches to calculate random errors. In themodel residuals approach, the random error is estimated by the difference of the flux observed minusthe flux predicted by a model (estimated, for example, by the ordinary least squared method if it is anempirical model [Richardson and Hollinger, 2005]). Then, the residuals (interpreted as random errors) couldbe characterized and tested for normality, homocedasticity, and independency [Richardson et al., 2008]. Inthat way, this approach evaluates the performance of an observed against a predicted measurement butmay be overestimating the calculation of random errors in measurements. Ideally, random errors shouldbe estimated in laboratory conditions, with two or more sensors measuring simultaneously in differenttreatments [Pihlatie et al., 2013; Pumpanen et al., 2004]. Nonetheless, the accuracy and precision also haveto be evaluated under field conditions. The field paired instruments approach assumes that measurements



are identical, there are no mechanical or calibration biases, and the differences between measurements arerelated to random errors [Billesbach, 2011]. Furthermore, this approach is expensive (e.g., deployment of twoeddy covariance towers) and has been used for short time periods (316 days) potentially loosing importantseasonal events (e.g., growing season, rewetting, and thawing) and could take more than a decade to beimplemented across networks [Schmidt et al., 2012]. Finally, the paired observation had been developedto minimize the difficulties of implementing the latter approaches to calculate random errors inmeasurements [Hollinger and Richardson, 2005; Hollinger et al., 2004; Richardson et al., 2012, 2006]. This is aversatile approach and minimizes the cost of implementation, but this method trades space for timeand results in the removal of many measurements that do not follow the requisite for similar days (seesection 2). This discussion highlights the need to develop and compare different approaches to estimateand characterize random errors across measurements of ecosystem fluxes.

5. Conclusions

There is increasing interest and need for an evaluation of uncertainties across monitoring networks andenvironmental observatories [He et al., 2010; Schmidt et al., 2012]. Thus, it is important to developapproaches to estimate uncertainty across different ecosystem measurements, including soil CO2 efflux (andother greenhouse gases), and across different vegetation types. This study presented results of randomerrors of soil CO2 efflux across four different types of ecosystems and a variety of weather conditions. Wemodified the paired observation approach to estimate random errors by including comparisons oftemperature and soil water content, which is an improvement and more strict than previous approachesthat used only soil water content [Savage et al., 2008]. The main findings of this study include the following:(a) the distribution of random errors is better explained by a double-exponential distribution, which ischaracterized by a tight central peak and long tails; and (b) the variation of random errors scales with themagnitude of the soil CO2 efflux rates but is independent of soil water conditions (). These results areimportant because knowing the properties of random errors could help to calculate confidence intervals forlocal-to-global carbon budgets, and a deeper understanding of random errors could improve model-datafusion approaches. We believe that future work needs to address the influence of random errors on gap-filling methods for soil CO2 efflux [e.g., Gomez-Casanovas et al., 2012; Richardson and Hollinger, 2007].

The development of different methodologies to estimate random errors in measurements is fundamental toimprove our understanding on how they influence carbon budgets. At the time, the estimation andcharacterization of random errors using the paired observation approach (or its variations) could result in aconvergence of results across different ecosystem fluxes, which may lead to a loss of information (ormisinformation) about random errors and the uncertainty in measurements. Finally, there is a need ofuncertainty assessments of other ecosystem fluxes (e.g., CH4 and NO2), not only in terrestrial ecosystemsbut also in marine and urban ecosystems and across different weather conditions to fully account for thecontribution of random errors in annual sums of greenhouse gas fluxes around the world.

ReferencesAnderson-Teixeira, K., J. P. Delog, A. M. Fox, D. A. Brese, and M. Litvak (2011), Differential responses of production and respiration to

temperature and moisture drive the carbon balance across a climatic gradient in New Mexico, Global Change Biol., 17, 410424,doi:10.1111/j.1365-2486.2010.02269.x.

Bahn, M., M. Schmitt, R. Siegwolf, A. Richter, and N. Bruggemann (2009), Does photosynthesis affect grassland soil-respired CO2 and itscarbon isotope composition on a diurnal timescale?, New Phytol., 182(2), 451460, doi:10.1111/j.1469-8137.2008.02755.x.

Bahn, M., I. A. Janssens, M. Reichstein, P. Smith, and S. E. Trumbore (2010a), Soil respiration across scales: Towards an integration of patternsand processes, New Phytol., 186, 292296, doi:10.1111/j.1469-8137.2010.03237.x.

Bahn,M., et al. (2010b), Soil respiration at mean annual temperature predicts annual total across vegetation types and biomes, Biogeosciences,7(7), 21472157, doi:10.5194/bg-7-2147-2010.

Baldocchi, D. (2008), Breathing of the terrestrial biosphere: Lessons learned from a global network of carbon dioxide flux measurementsystems, Aust. J. Bot., 56(1), 126, doi:10.1071/bt07151.

Baldocchi, D. D., J. Tang, and L. Xu (2006), How switches and lags in biophysical regulators affect spatial-temporal variation of soil respirationin an oak-grass savanna, J. Geophys. Res., 111, G02008, doi:10.1029/2005JG000063.

Billesbach, D. P. (2011), Estimating uncertainties in individual eddy covariance fluxmeasurements: A comparison of methods and a proposednew method, Agric. For. Meteorol., 151(3), 394405, doi:10.1016/j.agrformet.2010.12.001.

Bond-Lamberty, B., and A. Thomson (2010), Temperature-associated increases in the global soil respiration record, Nature, 464(7288),579582, doi:10.1038/nature08930.

Campbell, J. L., et al. (2013), Quantity is nothing without quality: Automated QA/QC for streaming environmental sensor data, BioScience,63(7), 574585, doi:10.1525/bio.2013.63.7.10.



AcknowledgmentsA.C. acknowledges support from ascholarship and support for an academicexchange with the University of Delawareprovided by CONACyT (CVU 397284).M.B. acknowledges support from theAustrian Science Fund (FWF) grantsP18756-B16 and P22214-B17. M.L.acknowledges support from grantDOE University-Lab EPSCoR DE-FG02-08ER46506 and DOE BER DE-SC0008088and the Sevilleta LTER. J.P. acknowledgessupport from the Academy of Finlandprojects 218094 and 213093 as well asthe Academy of Finland Finnish Centre ofExcellence Program. R.V. acknowledgesgrant support from CONACyT CienciaBasica-152671, NASA NNX13AQ06G,and USDA 2014-67003-22070. This workcontributes to the efforts of the NorthAmerican Carbon Program. For datarequests and algorithms to calculaterandom errors please email RodrigoVargas ([email protected]).

http://dx.doi.org/10.1111/j.1365-2486.2010.02269.xhttp://dx.doi.org/10.1111/j.1469-8137.2008.02755.xhttp://dx.doi.org/10.1111/j.1469-8137.2010.03237.xhttp://dx.doi.org/10.5194/bg-7-2147-2010http://dx.doi.org/10.1071/bt07151http://dx.doi.org/10.1029/2005JG000063http://dx.doi.org/10.1016/j.agrformet.2010.12.001http://dx.doi.org/10.1038/nature08930http://dx.doi.org/10.1525/bio.2013.63.7.10

Cueva, A., M. Bahn, J. Pumpanen, and R. Vargas (2012), A multisite and multi-model analysis of random errors in soil CO2 efflux across soilwater conditions, AGU Fall Meeting Abstracts, 1,0284.

Dragoni, D., H. P. Schmid, C. S. B. Grimmond, and H. W. Loescher (2007), Uncertainty of annual net ecosystem productivity estimated usingeddy covariance flux measurements, J. Geophys. Res., 112, D17102, doi:10.1029/2006JD008149.

Enquist, B. J., E. P. Economo, T. E. Huxman, A. P. Allen, D. D. Ignace, and J. F. Gillooly (2003), Scaling metabolism from organisms to ecosys-tems, Nature, 423(6940), 639642.

Foley, J. A., M. H. Costa, C. Delire, N. Ramankutty, and P. Snyder (2003), Green surprise? How terrestrial ecosystems could affect Earths climate,Front. Ecol. Environ., 1(1), 3844.

Glinski, J., and W. Stepniewski (1985), Soil Aeration and Its Role for Plants, CRC Press, Boca Raton, Fla.Gomez-Casanovas, N., K. Anderson-Teixeira, M. Zeri, C. J. Bernacchi, and E. H. Delucia (2012), Gap filling strategies and error in estimating

annual soil respiration, Global Change Biol., 19(6), 19411952, doi:10.1111/gcb.12127.Hagen, S. C., B. H. Braswell, E. Linder, S. Frolking, A. D. Richardson, and D. Y. Hollinger (2006), Statistical uncertainty of eddy fluxbased

estimates of gross ecosystem carbon exchange at Howland Forest, Maine, J. Geophys. Res., 111 D08S03, doi:10.1029/2005JD006154.Hanson, P. J., N. T. Edwards, C. T. Garten, and J. A. Andrews (2000), Separating root and soil microbial contributions to soil respiration:

A review of methods and observations, Biogeochemistry, 48(1), 115146, doi:10.1023/A:1006244819642.He, H., et al. (2010), Uncertainty analysis of eddy flux measurements in typical ecosystems of ChinaFLUX, Ecol. Inf., 5, 492502, doi:10.1016/

j.ecoinf.2010.07.004.Heimann, M., and M. Reichstein (2008), Terrestrial ecosystem carbon dynamics and climate feedbacks, Nature, 451(7176), 289292,

doi:10.1038/nature06591.Hirano, T., H. Kim, and Y. Tanaka (2003), Long-term half-hourly measurement of soil CO2 concentration and soil respiration in a temperate

deciduous forest, J. Geophys. Res., 108(D20), 4631, doi:10.1029/2003JD003766.Hollinger, D. Y., and A. D. Richardson (2005), Uncertainty in eddy covariance measurements and its application to physiological models,

Tree Physiol., 25, 873885, doi:10.1093/treephys/25.7.873.Hollinger, D. Y., et al. (2004), Spatial and temporal variability in forest-atmosphere CO2 exchange, Global Change Biol., 10(10), 16891706,

doi:10.1111/j.1365-2486.2004.00847.x.Jassal, R. S., A. T. Black, M. D. Novak, K. Morgenstern, Z. Nesic, and D. Gaumont-Guay (2005), Relationship between soil CO2 concentrations

and forest-floor CO2 effluxes, Agric. For. Meteorol., 130, 176192, doi:10.1016/j.agrformet.2005.03.005.Kessomkiat, W., H.-J. H. Franssen, A. Graf, and H. Vereecken (2013), Estimating random errors of eddy covariance data: An extended two-tower

approach, Agric. For. Meteorol., 171172, 203219, doi:10.1016/j.agrformet.2012.11.019.Kim, D. G., R. Vargas, B. Bond-Lamberty, and M. R. Turetsky (2012), Effects of soil rewetting and thawing on soil gas fluxes: A review of current

literature and suggestions for future research, Biogeosciences, 9(7), 24592483, doi:10.5194/bg-9-2459-2012.Knapp, A. K., et al. (2008), Consequences of more extreme precipitation regimes for terrestrial ecosystems, BioScience, 58(9), 811821,

doi:10.1641/B580908.Kuzyakov, Y. (2002), Factors affecting rhizosphere priming effects, J. Plant Nutr. Soil Sci., 165, 382396, doi:10.1002/1522-2624(200208)

165:43.0.CO;2-#.Kuzyakov, Y. (2006), Sources of CO2 efflux from soil and review of partitioning methods, Soil Biol. Biochem., 38(3), 425448, doi:10.1016/

j.soilbio.2005.08.020.Lasslop, G., M. Reichstein, J. Kattge, and D. Papale (2008), Influences of observation errors in eddy flux data on inverse model parameter

estimation, Biogeosciences, 5, 13111324, doi:10.5194/bg-5-1311-2008.Leon, E., R. Vargas, S. H. Bullock, E. Lopez, A. R. Panosso, and N. La Scala Jr (2014), Hot spots, hot moments, and spatio-temporal controls on

soil CO2 efflux in a water-limited ecosystem, Soil Biol. Biochem., 77, 1221, doi:10.1016/j.soilbio.2014.05.029.Liu, M., H. He, G. Yu, Y. Luo, X. Sun, and H. Wang (2009), Uncertainty analysis of CO2 flux components in sub-tropical evergreen coniferous

plantation, Sci. China Ser. D: Earth Sci., 52(2), 257268, doi:10.1007/s11430-009-0010-6.Loescher, H. W., B. E. Law, L. Mahrt, D. Y. Hollinger, J. Campbell, and S. C. Wofsy (2006), Uncertainties in, and interpretation of, carbon flux

estimates using the eddy covariance technique, J. Geophys. Res., 111, D21S90, doi:10.1029/2005JD006932.Loik, M. E., D. D. Breshears, W. K. Lauenroth, and J. Belnap (2004), A multi-scale perspective of water pulses in dryland ecosystems: Climatology

and ecohydrology of the western USA, Oecologia, 141(2), 269281, doi:10.1007/s00442-004-1570-y.Maier, M., and H. Schack-Kirchner (2014), Using the gradient method to determine soil gas flux: A review, Agric. For. Meteorol., 192193, 7895,

doi:10.1016/j.agrformet.2014.03.006.Menzer, O., A. M. Moffat, W. Meiring, G. Lasslop, E. G. Schukat-Talamazzini, and M. Reichstein (2013), Random errors in carbon and water

vapor fluxes assessed with Gaussian processes, Agric. For. Meteorol., 178179, 161172, doi:10.1016/j.agrformet.2013.04.024.Moldrup, P., T. Olesen, T. Yamaguchi, P. Schjnning, and D. E. Rolston (1999), Modeling diffusion and reaction in soils: IX. The Buckingham-

Burdine-Campbell equation for gas diffusivity in undisturbed soil, Soil Sci., 164(8), 542551.Moyano, F. E., et al. (2012), The moisture response of soil heterotrophic respiration: Interaction with soil properties, Biogeosciences, 9, 11731182,

doi:10.5194/bg-9-1173-2012.Pihlatie, M. K., et al. (2013), Comparison of static chambers to measure CH4 emissions from soils, Agric. For. Meteorol., 171172, 124136,

doi:10.1016/j.agrformet.2012.11.008.Pingintha, N., M. Y. Leclerc, J. P. Beasley Jr., G. Zhang, and C. Senthong (2010), Assessment of the soil CO2 gradient method for soil CO2

efflux measurements: Comparison of six models in the calculation of the relative gas diffusion coefficient, Tellus B, 62(1), 4758,doi:10.1111/j.1600-0889.2009.00445.x.

Pumpanen, J., H. Ilvesniemi, and P. Hari (2003), A process-based model for predicting soil carbon dioxide efflux and concentration, Soil Sci.Soc. Am. J., 67, 402413, doi:10.2136/sssaj2003.4020.

Pumpanen, J., et al. (2004), Comparison of different chamber techniques for measuring soil CO2 efflux, Agric. For. Meteorol., 123(34),159176, doi:10.1016/j.agrformet.2003.12.001.

Pumpanen, J., H. Ilvesniemi, L. Kulmala, E. Siivola, H. Laakso, P. Kolari, C. Helenelund, M. Laakso, M. Uusimaa, and P. Hari (2008), Respiration inboreal forest soil as determined from carbon dioxide concentration profile, Soil Sci. Soc. Am. J., 72(5), 11871196, doi:10.2136/sssaj2007.0199.

Regan, H. M., M. Colyvan, and M. A. Burgman (2002), A taxonomy and treatment of uncertainty for ecology and conservation biology,Ecol. Appl., 12(2), 618628, doi:10.1890/1051-0761(2002)012[0618:ATATOU]2.0.CO;2.

Reich, P. B., M. G. Tjoelker, J. L. Machado, and J. Oleksyn (2006), Universal scaling of respiratory metabolism, size and nitrogen in plants,Nature, 439(7075), 457461.

Reichstein, M., et al. (2003), Modeling temporal and large-scale spatial variability of soil respiration from soil water availability, temperatureand vegetation productivity indices, Global Biogeochem. Cycles, 17(4), 1104, doi:10.1029/2003GB002035.



http://dx.doi.org/10.1029/2006JD008149http://dx.doi.org/10.1111/gcb.12127http://dx.doi.org/10.1029/2005JD006154http://dx.doi.org/10.1023/A:1006244819642http://dx.doi.org/10.1016/j.ecoinf.2010.07.004http://dx.doi.org/10.1016/j.ecoinf.2010.07.004http://dx.doi.org/10.1038/nature06591http://dx.doi.org/10.1029/2003JD003766http://dx.doi.org/10.1093/treephys/25.7.873http://dx.doi.org/10.1111/j.1365-2486.2004.00847.xhttp://dx.doi.org/10.1016/j.agrformet.2005.03.005http://dx.doi.org/10.1016/j.agrformet.2012.11.019http://dx.doi.org/10.5194/bg-9-2459-2012http://dx.doi.org/10.1641/B580908http://dx.doi.org/10.1002/1522-2624(200208)165:43.0.CO;2-#http://dx.doi.org/10.1002/1522-2624(200208)165:43.0.CO;2-#http://dx.doi.org/10.1002/1522-2624(200208)165:43.0.CO;2-#http://dx.doi.org/10.1002/1522-2624(200208)165:43.0.CO;2-#http://dx.doi.org/10.1016/j.soilbio.2005.08.020http://dx.doi.org/10.1016/j.soilbio.2005.08.020http://dx.doi.org/10.5194/bg-5-1311-2008http://dx.doi.org/10.1016/j.soilbio.2014.05.029http://dx.doi.org/10.1007/s11430-009-0010-6http://dx.doi.org/10.1029/2005JD006932http://dx.doi.org/10.1007/s00442-004-1570-yhttp://dx.doi.org/10.1016/j.agrformet.2014.03.006http://dx.doi.org/10.1016/j.agrformet.2013.04.024http://dx.doi.org/10.5194/bg-9-1173-2012http://dx.doi.org/10.1016/j.agrformet.2012.11.008http://dx.doi.org/10.1111/j.1600-0889.2009.00445.xhttp://dx.doi.org/10.2136/sssaj2003.4020http://dx.doi.org/10.1016/j.agrformet.2003.12.001http://dx.doi.org/10.2136/sssaj2007.0199http://dx.doi.org/10.1890/1051-0761(2002)012[0618:ATATOU]2.0.CO;2http://dx.doi.org/10.1029/2003GB002035

Reichstein, M., et al. (2013), Climate extremes and the carbon cycle, Nature, 500(7462), 287295, doi:10.1038/nature12350.Richardson, A. D., and D. Y. Hollinger (2005), Statistical modeling of ecosystem respiration using eddy covariance data: Maximum likelihood

parameter estimation, and Monte Carlo simulation of model and parameter uncertainty, applied to three simplemodels, Agric. For. Meteorol.,131(34), 191208, doi:10.1016/j.agrformet.2005.05.008.

Richardson, A. D., and D. Y. Hollinger (2007), A method to estimate the additional uncertainty in gap-filled NEE resulting from long gaps inthe CO2 flux record, Agric. For. Meteorol., 147(34), 199208, doi:10.1016/j.agrformet.2007.06.004.

Richardson, A. D., et al. (2006), A multi-site analysis of random error in tower-based measurements of carbon and energy fluxes, Agric. For.Meteorol., 136, 118, doi:10.1016/j.agrformet.2006.01.007.

Richardson, A. D., et al. (2008), Statistical properties of random CO2 flux measurement uncertainty inferred from model residuals, Agric. For.Meteorol., 148(1), 3850, doi:10.1016/j.agrformet.2007.09.001.

Richardson, A. D., M. Aubinet, A. Barr, D. Y. Hollinger, A. Ibrom, G. Lasslop, andM. Reichstein (2012), Uncertainty quantification, in Eddy Covariance:A Practical Guide to Measurement and Data Analysis, edited by M. Aubinet, T. Vesala, and D. Papale, pp. 173209, Springer, Netherlands,doi:10.1007/978-94-007-2351-17.

Ryan, M. G., and B. E. Law (2005), Interpreting, measuring, and modeling soil respiration, Biogeochemistry, 73(1), 327, doi:10.1007/s10533-004-5167-7.

Savage, K., E. A. Davidson, and A. D. Richardson (2008), A conceptual and practical approach to data quality and analysis procedures forhigh-frequency soil respiration measurements, Funct. Ecol., 22, 10001007, doi:10.1111/j.1365-2435.2008.01414.x.

Schmidt, A., C. Hanson, W. S. Chan, and B. E. Law (2012), Empirical assessment of uncertainties of meteorological parameters and turbulentfluxes in the AmeriFlux network, J. Geophys. Res., 117, G0414, doi:10.1029/2012JG002100.

imnek, J., and D. L. Suarez (1993), Modelling of carbon dioxide transport and production in soil: 1. Model development,Water Resour. Res.,29(2), 487497, doi:10.1029/92WR02225.

Tang, J., D. D. Baldocchi, Y. Qi, and L. Xu (2003), Assessing soil CO2 efflux using continuous measurements of CO2 profiles in soils with smallsolid-state sensors, Agric. For. Meteorol., 118(34), 207220, doi:10.1016/s0168-1923(03)00112-6.

Troeh, F. R., J. D. Jabro, and D. Kirkham (1982), Gaseous diffusion equations for porous materials, Geoderma, 27, 239253, doi:10.1016/0016-7061(82)90033-7.

Vargas, R. (2012), How a hurricane disturbance influences extreme CO2 fluxes and variance in a tropical forest, Environ. Res. Lett., 7(3), 035704,doi:10.1088/1748-9326/7/3/035704.

Vargas, R., and M. F. Allen (2008), Dynamics of fine root, fungal rhizomorphs, and soil respiration in a mixed temperate forest: Integratingsensors and observations, Vadose Zone J., 7(3), 10551064, doi:10.2136/vzj2007.0138.

Vargas, R., et al. (2010), Looking deeper into the soil: Biophysical controls and seasonal lags of soil CO2 production and efflux, Ecol. Appl.,20(6), 15691582.

Vargas, R., M. S. Carbone, M. Reichstein, and D. D. Baldocchi (2011a), Frontiers and challenges in soil respiration research: Frommeasurements tomodel-data integration, Biogeochemistry, 102, 113, doi:10.1007/s10533-010-9462-1.

Vargas, R., D. D. Baldocchi, M. Bahn, P. J. Hanson, K. P. Hosman, L. Kulmala, J. Pumpanen, and B. Yang (2011b), On the multi-temporalcorrelation between photosynthesis and soil CO2 efflux: Reconciling lags and observations, New Phytol., 191(4), 10061017,doi:10.1111/j.1469-8137.2011.03771.x.

Vargas, R., S. L. Collins, M. L. Thomey, J. E. Johnson, R. F. Brown, D. O. Natvig, and M. T. Friggens (2012), Precipitation variability and fire influencethe temporal dynamics of soil CO2 efflux in an arid grassland, Global Change Biol., 18(4), 14011411, doi:10.1111/j.1365-2486.2011.02628.x.

Vargas, R., et al. (2013), Drought influences the accuracy of simulated ecosystem fluxes: A model-data meta-analysis for Mediterranean OakWoodlands, Ecosystems, 16, 749764, doi:10.1007/s10021-013-9648-1.

Vicca, S., et al. (2014), Can current moisture responses predict soil CO2 efflux under altered precipitation regimes? A synthesis of manipulationexperiments, Biogeosciences, 11, 29913013, doi:10.5194/bg-11-2991-2014.

Wohlfahrt, G., A. Hammerle, A. Haslwanter, M. Bahn, U. Tappeiner, and A. Cernusca (2008), Seasonal and inter-annual variability of the netecosystem CO2 exchange of a temperate mountain grassland: Effects of weather and management, J. Geophys. Res., 113, D08110,doi:10.1029/2007JD009286.

Xu, L., D. D. Baldocchi, and J. Tang (2004), How soil moisture, rain pulses, and growth alter the response of ecosystem respiration totemperature, Global Biogeochem. Cycles, 18, GB4002, doi:10.1029/2004GB002281.



http://dx.doi.org/10.1038/nature12350http://dx.doi.org/10.1016/j.agrformet.2005.05.008http://dx.doi.org/10.1016/j.agrformet.2007.06.004http://dx.doi.org/10.1016/j.agrformet.2006.01.007http://dx.doi.org/10.1016/j.agrformet.2007.09.001http://dx.doi.org/10.1007/978-94-007-2351-17http://dx.doi.org/10.1007/s10533-004-5167-7http://dx.doi.org/10.1007/s10533-004-5167-7http://dx.doi.org/10.1111/j.1365-2435.2008.01414.xhttp://dx.doi.org/10.1029/2012JG002100http://dx.doi.org/10.1029/92WR02225http://dx.doi.org/10.1016/s0168-1923(03)00112-6http://dx.doi.org/10.1016/0016-7061(82)90033-7http://dx.doi.org/10.1016/0016-7061(82)90033-7http://dx.doi.org/10.1088/1748-9326/7/3/035704http://dx.doi.org/10.2136/vzj2007.0138http://dx.doi.org/10.1007/s10533-010-9462-1http://dx.doi.org/10.1111/j.1469-8137.2011.03771.xhttp://dx.doi.org/10.1111/j.1365-2486.2011.02628.xhttp://dx.doi.org/10.1007/s10021-013-9648-1http://dx.doi.org/10.5194/bg-11-2991-2014http://dx.doi.org/10.1029/2007JD009286http://dx.doi.org/10.1029/2004GB002281

/ColorImageDict > /JPEG2000ColorACSImageDict > /JPEG2000ColorImageDict > /AntiAliasGrayImages false /CropGrayImages false /GrayImageMinResolution 300 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.00000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict > /GrayImageDict > /JPEG2000GrayACSImageDict > /JPEG2000GrayImageDict > /AntiAliasMonoImages false /CropMonoImages false /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 400 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.00000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict > /AllowPSXObjects true /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile (None) /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False

/CreateJDFFile false /Description > /Namespace [ (Adobe) (Common) (1.0) ] /OtherNamespaces [ > > /FormElements true /GenerateStructure false /IncludeBookmarks false /IncludeHyperlinks false /IncludeInteractive false /IncludeLayers false /IncludeProfiles true /MarksOffset 6 /MarksWeight 0.250000 /MultimediaHandling /UseObjectSettings /Namespace [ (Adobe) (CreativeSuite) (2.0) ] /PDFXOutputIntentProfileSelector /DocumentCMYK /PageMarksFile /RomanDefault /PreserveEditing true /UntaggedCMYKHandling /UseDocumentProfile /UntaggedRGBHandling /UseDocumentProfile /UseDocumentBleed false >> ]>> setdistillerparams> setpagedevice

Documents

A multisite analysis of temporal random errors in soil CO2 ...udel.edu/~rvargas/Vargas/Publications_files/Cueva_etal_2015_JGR... · A multisite analysis of temporal random errors